FIG. 1 illustrates an exemplary configuration from the prior art using a liquid crystal-based phase modulator 1 that can be used to correct certain aberrations of a laser beam Fa and do so at the focal point of a lens 3. This device thus also comprises phase measuring means 2 and feedback means in a feedback loop Br that make it possible to occasionally correct the phase of the incident beam to correct its aberrations and supply a corrected beam Fc. The phase is directly linked to the optical index seen by a light beam and this is directly expressed in the following relationship:φ=2πn(λ)z/λ, with z being the distance travelled by the beam in the medium.
One of the main characteristics of liquid crystal cells lies in the fact that it is possible to cause the optical index of the medium to be changed by the application of an electrical field. In effect, the liquid crystal molecules, notably nematic molecules have an ordinary optical axis and an extraordinary optical axis which are respectively along the directing vector D and perpendicular to said directing vector D, as is represented in FIG. 2. These molecules can be oriented under the action of an applied electrical field and the three positions (a), (b) and (c) represented in FIG. 2 respectively relate to a weak field (below the field needed to be able to begin orienting the molecules), an average field and a strong field.
By changing the orientation of said molecules, it thus becomes possible to vary the average optical index seen by a light beam passing through the medium. Generally, an untwisted nematic of positive or negative dielectric anisotropy is used, integrated in a cell more specifically comprising a polarizer at the input, two substrates, one of which, by virtue of a prior surface state, makes it possible to constrain the molecules in an initial state.
Such a device operates with a light that is polarized in the axis of the director of the liquid crystals. In the case of a positive dielectric anisotropy, light at the input of the device sees the extraordinary index of the liquid crystal when the device is at rest (zero voltage), and, as the field increases, with the liquid crystal molecules straightening, the light sees an intermediate index between the ordinary and extraordinary index. To modify the phase of an unpolarized light, this phase-shifting operation must be performed on both components of the electrical field, and for this, it is possible either to superpose two devices as described in the article: Polarization-independent liquid crystal phase modulator using a thin polymer-separated double-layered structure, by Yi-Hsin Lin, Hongwen Ren, Yung Hsun Wu, Zhibing Ge and Shin-Tson Wu: College of Optics and Photonics, University of Central Florida, Orlando, Fla., 32816 and Yue Zhao and Jiyu Fang: Advanced Materials Processing and Analysis Center and Department of Mechanical Materials, or to use a quarter-wave plate and a mirror and thus cause the light to pass twice in the same device thus acting on the two components of the electrical field as described in the article: Liquid-crystal phase modulator for unpolarized light by Gordon D, Love, APPLIED OPTICS/Vol. 32, No. 13/1 May 1993.
In the first case, the superposition poses major parallax problems and therefore does not allow for the superposition of matrices with small pixels. In the second case, the use of a reflector in the optical path makes it into a reflection device which cannot therefore be integrated in a conventional optic (optical zoom for imager for example).
Also known are liquid crystal cells of cholesteric type in which the molecules are not arranged exactly parallel to one another but adopt a helical configuration. If a cross-section is taken in the structure along a plane perpendicular to the axis z of the spiral, the distortion of the molecules in the plane is similar to that of a nematic but the preferred direction of orientation of the molecules turns slowly when moving along the axis z. A periodic helical structure is thus obtained along the direction z perpendicular to the plane of the layers. Depending on the illumination wavelength and the pitch of the helix, such structures may behave partially as mirrors if the following condition is verified:
p=λ/n with λ being the wavelength of the wave and n being the index of the liquid crystal medium.
Generally, the liquid crystals of cholesteric type are spontaneously oriented in a preferred direction n of the space that is called the director. When an applied electrical field has constrained them in a certain orientation, the molecules have a tendency to revert to this state in response to a deformation.
A deformation can be broken down into three distortions. In fact, in response to a deformation, a liquid crystal molecule undergoes a pair of forces which have the effect of opposing it so as to revert to the state in which all the molecules are aligned. Furthermore, when an electrical field is applied to said molecules, the molecules have a tendency to be aligned parallel to the field because of the polarization of the molecules.
There is then competition between the effect of alignment parallel to the electrical field and the elastic properties of the medium. It can be considered that the elastic deformations of liquid crystal molecules are of three types:
fan out deformation;
torsional deformation;
twist deformation, also called twisting.
These three types of deformation are illustrated in FIG. 3.
The diagram of FIG. 4 illustrates the existence of the different possible states, upon the application of an electrical field and upon the progressive elimination of the application of an electrical field.
More specifically:                the so-called “planar” state P corresponds to a state in which the molecules are in a helix with a vertical axis;        the so-called “focal conical” state CP corresponds to a state in which, for liquid crystal molecules with positive dielectric anisotropy, in the axis of the helix, there is a perpendicular epsilon below the mean epsilon of the direction perpendicular to the plane of the electrodes. Under voltage, the helix, before being deformed, tends to lie down;        the so-called “homeotropic” state H corresponds to a state in which all the molecules are vertical, coming directly from the “planar” state or else from the “focal conical” state for which the pitch will gradually increase until it is completely unwound;        the “transient planar” state PT corresponds to a “planar” state for which the pitch is greater than the initial pitch.        
The “planar”/“homeotropic” transition has been studied in more detail. The liquid crystal molecules form a helical structure with a helix axis perpendicular to the plane of the layers. The so-called polar angle θ that the molecules form with this axis tends to increase with a reduction of the applied electrical field. When this angle is equal to π/2, the molecules are in a so-called planar structure.
In this approach, it is considered that the polar angle θ is independent of the axis z and that the azimuthal angle φ varies along the axis z with a constant q relative to the wave vector of the helix, in such a way that the “twist” parameter is constant, these angles being represented in FIG. 5.
The components of the directing vector n of a molecule are thus given by the following formulae:nx=sin θ cos(qz),ny=sin θ sin(qz) and nz=cos θ
The free energy is given by the following formula:f=½K22(q0−q sin2θ)+½K33q2 sin2θ cos2θ+½Δ∈∈0E2 sin2θq0, corresponds to the constant with zero electrical field;the pitch of the helix p being equal to π/q.
The constants K22 and K33 corresponding to the torsion and “twist” elastic constants.
By using the following parameters:K3=K33/K22,ψ=f/K22q02, and e=E/Ec The following equation is obtained:ψ=½(1−λ sin2θ)+½K3ψ2 sin2θ cos2θ+½(π/2e)2 sin2θ
By seeking to minimize the parameter ψ, the following is obtained:λ=1/(sin2θ+K3 cos2θ)andq=q0/(sin2θ+K3 cos2θ)
When the polar angle θ is very small, it can be considered that:q=q0/K3=(K22/K33)q0 and therefore the pitch of the helix p=(K22/K33)p0 
For most of the known liquid crystals, the rate K33/K22 is greater than 1, even of the order of 2. A pitch of the helix is thus obtained which is of the order of 2 times the initial pitch p0 of the helix. With, in addition, a very small polar angle θ, the following equation can be obtained:
      ψ    =                  1        2            +                        1          2                ⁢                  sin          2                ⁢                  θ          ⁡                      [                                                            (                                                            π                      2                                        ⁢                    e                                    )                                2                            -                              1                                                      K                    ⁢                                                                                  ⁢                    3                                    +                                                            (                                              1                        -                                                  K                          ⁢                                                                                                          ⁢                          3                                                                    )                                        ⁢                                          sin                      2                                        ⁢                    θ                                                                        ]                                          E      c        =                            π          2                          P          0                    ⁢                        (                                    K              22                                                      ɛ                0                            ⁢              Δ              ⁢                                                          ⁢              ɛ                                )                          1          /          2                    To analyze whether it is possible to have a stable state in a conical helix structure, the second derivative of the function ψ is studied:The second derivative relative to the angle θ (or sin2θ) is written:
                    ∂        2            ⁢      ψ              ∂                        (                                    sin              2                        ⁢            θ                    )                2              =            K      ⁡              (                  1          -          K                )                            [                  K          +                                    (                              1                -                K                            )                        ⁢                          sin              2                        ⁢            θ                          ]            2      And, effectively, if K33>K22, 1−K is negative whatever the angle θ and therefore the energy is a curve with downward concavity and does not show any minimum therefore stable state as is illustrated by FIG. 6.